Advertisements
Advertisements
प्रश्न
If a : b : : c : d, then prove that
(ax+ by): (cx + dy)=(ax - by) : (cx - dy)
बेरीज
Advertisements
उत्तर
(ax+ by): (cx + dy)=(ax - by) : (cx - dy)
`"a"/"b" = "c"/"d"`
Multiplying both sides by `"x"/"y"`
`=> "a"/"b" xx "x"/"y" = "c"/"d" xx "x"/"y"`
`=> ("ax")/("by") = ("cx")/("dy")`
Applying componendo and dividendo,
`("ax+ by")/("ax - by") = ("cx + dy")/("cx - dy")`
` => ("ax+ by")/("cx + dy") = ("ax - by")/("cx - dy")`
Hence, ax + by : cx + dy = ax - by : cx - dy
shaalaa.com
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
